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Uncovered Interest Rate Parity and the Term Structure of Interest Rates Journal of International Money and Finance 26 (2007) 1038e1069 www.elsevier.com/locate/jimf Uncovered interest rate parity and the term structure Geert Bekaert a,*, Min Wei b, Yuhang Xing c a Columbia Business School, 808 Uris Hall, 3022 Broadway, New York, NY 10027, USA b Board of Governors of the Federal Reserve, Division of Monetary Affairs, Washington, DC 20551, USA c Jones Graduate School of Management, Rice University, Room 230, MS531, 6100 Main Street, Houston, TX 77005, USA Abstract This paper examines uncovered interest rate parity (UIRP) and the expectations hypotheses of the term structure (EHTS) at both short and long horizons. The statistical evidence against UIRP is mixed and is currency- not horizon-dependent. Economically, the deviations from UIRP are less pronounced than previously documented. The evidence against the EHTS is statistically more uniform, but, economically, actual spreads and theoretical spreads (spreads constructed under the null of the EHTS) do not behave very differently, especially at long horizons. Partly because of this, the deviations from the EHTS only play a minor role in explaining deviations from UIRP at long horizons. Ó 2007 Elsevier Ltd. All rights reserved. JEL classification: E4; F3; C5 Keywords: Foreign exchange; Term structure; Uncovered interest rate parity; Expectations hypotheses; Unbiasedness hypothesis 1. Introduction Uncovered interest rate parity (UIRP) predicts that high yield currencies should be expected to depreciate. It also predicts that, ceteris paribus, a real interest rate increase should appreciate the currency. UIRP is one of the cornerstones of international finance, constituting an important building block of most important exchange rate determination theories such as the monetary * Corresponding author. Tel.: +1 212 854 9156; fax: +1 212 662 8474. E-mail addresses: [email protected] (G. Bekaert), [email protected] (M. Wei), [email protected] (Y. Xing). 0261-5606/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jimonfin.2007.05.004 G. Bekaert et al. / Journal of International Money and Finance 26 (2007) 1038e1069 1039 exchange rate model, Dornbusch’s (1976) overshooting model or Krugman’s (1991) target zone model and dominating the discussion on exchange rate determination in most international text- books. Nevertheless, there appears to be overwhelming empirical evidence against UIRP, at least at frequencies less than 1 year (see Bekaert and Hodrick, 1993; Engel, 1996; Froot and Thaler, 1990; Mark and Wu, 1998). Given that this empirical evidence has not stopped theorists from relying on UIRP, it is fortunate that recent evidence is more favorable: Bekaert and Ho- drick (2001) and Baillie and Bollerslev (2000) argue that doubtful statistical inference may have contributed to the strong rejections of UIRP at higher frequencies whereas Chinn and Mer- edith (2004) marshal evidence that UIRP holds much better at long horizons. Chaboud and Wright (2005) investigate overnight exchange rate movements and interest-rate differentials and also find support for UIRP. It seems rather difficult to find a coherent story to explain all these results. Short-term de- viations of UIRP may occur while long-horizon UIRP holds (see Froot and Thaler, 1990), if inefficient markets or short-term market frictions prevent an immediate complete response of the exchange rate to an interest rate change. However, both the theoretical and the empirical results seem puzzling on second thought. First, it is hard to reconcile the high frequency Chaboud and Wright (2005) results, the stan- dard rejections at weekly or monthly frequencies and the long-term evidence from this fric- tions-perspective. In fact, the presence of speculative capital of various proprietary desks in foreign exchange markets attempting to exploit deviations from UIRP (see Green, 1992 for an illustration) suggests that it might be the long-term relation rather than the short-term re- lation that is affected by market frictions, since it is unlikely that these trading desks will keep capital tied up in such long-term contracts. Second, by construction, if UIRP holds in the short run, it should hold in the long run as long as the expectations hypotheses of the term structure of interest rates (EHTS) holds; that is, as long as the long rate equals the average expected future short rate over the life of the bond. It seems unlikely that the short-term deviations from UIRP would exactly offset the long-term deviations from the EHTS to make UIRP hold in the long run. In alternative models based on risk, a time-varying risk premium separates expected exchange rate changes from the interest differential and a time-varying term premium separates the long-term interest rate from expected future short rates. Consequently, these risk premiums would be driven by the same fundamentals and de- viations from UIRP and the EHTS should be visible at both long and short horizons. Such a story is potentially consistent with the Chaboud and Wright (2005) results as they focus on observations where exchange risk is minimal (but interest is still paid) and the risk pre- mium may vanish. It is therefore worthwhile to re-examine UIRP and the EHTS simultaneously at long and short horizons. To do so, our main tool of analysis will be a vector autoregression (VAR) on exchange rate changes, interest rates and term spreads, drawing data from three countries: the US, the UK and Germany. The VAR not only allows us to disentangle the various hypotheses in a unified framework, it also makes it easy to conduct more powerful joint tests across both short and long horizons. Clarida and Taylor (1997) and Clarida et al. (2003) show that for- ward premiums of different maturities are helpful in forecasting exchange rates. We also in- clude long-term spreads (of a 5-year maturity) in the VAR. Apart from the statistical significance, we also examine the economic significance of potential deviations from UIRP and the EHTS. Many policy makers conduct policy experiments imposing the EHTS for ex- ample (see Evans, 1998; Bernanke et al., 1997). If the EHTS does not hold statistically, but the spread as predicted by the EHTS and the actual spread are very highly correlated, 1040 G. Bekaert et al. / Journal of International Money and Finance 26 (2007) 1038e1069 assuming the EHTS in a policy analysis may be acceptable. Our framework allows us to in- vestigate the economic significance of imposing different hypotheses. Our main findings can be summarized as follows. The statistical evidence regarding UIRP is more mixed than previously thought and it depends on the currency pair but not on the horizon. Economically, although our statistics show that UIRP deviations are im- portant, it is crucial to adjust them for small-sample biases. Our results here are of imme- diate relevance for a growing literature in international economics that makes use of an empirically calibrated ‘‘deviation from UIRP’’, see for example McCallum (1994).In comparison, the statistical evidence against the EHTS is more uniform across countries and horizons. Finally, the deviations from the EHTS are not economically important, indi- cating that analyzing the effects of policy experiments under the null of the EHTS may be useful. The remainder of the paper is organized as follows. Section 2 reviews the main hypotheses, UIRP and the EHTS, and how they are related. Section 3 outlines our econometric procedure. Sections 4 and 5 present empirical results from the statistical and the economic perspective. Section 6 focuses on smaller VARs using Japanese data, for which we lack truly long-term zero-coupon rates. Section 7 concludes. 2. Expectations hypotheses 2.1. Uncovered interest rate parity (UIRP) UIRP holds at the n-period horizon if 1 ðE s À s Þ¼i À ià þ a ð1Þ n t tþn t t;n t;n n where st is the logarithm of the spot exchange rate (local per foreign currency), it,n and it*,n are the time-t continuously compounded domestic and foreign n-period interest rate, respec- tively, and an is a constant risk premium. All interest rates are expressed in monthly rates. Denote Dst ¼ st À stÀ1. UIRP can be tested with the following regression: Xn À Á 1 uirp à Dstþi ¼ an þ bn it;n À it;n þ 3t;tþn ð2Þ n i¼1 Under the null the slope coefficient equals one. 2.2. Expectations hypotheses of the term structure (EHTS) The EHTS holds if the long-term n-period interest rate it,n is an unbiased estimator of the average expected short-term interest rate it+h,1 during the bond’s life plus a constant term premium: 1 XnÀ1 it;n ¼ Etðitþh;1Þþcn ð3Þ n h¼0 G. Bekaert et al. / Journal of International Money and Finance 26 (2007) 1038e1069 1041 A direct test of this hypothesis (see for example Campbell and Shiller, 1991) is the regression: XkÀ1 À Á 1 ehts itþim;m À it;m ¼ an þ bn;m it;n À it;m þ utþnÀm ð4Þ k i¼0 where k ¼ n/m and m < n. Under the EHTS, the slope coefficient in this regression should equal one.1 2.3. UIRP and EHTS UIRP at horizon n is implied by UIRP at the short horizon (m periods, say) and the EHTS at horizon n. To see this, assume that the UIRP holds at the shorter-term m-period horizon: Xm 1 à EtDstþj ¼ am þ it;m À it;m ð5Þ m j¼1 and that the EHTS holds at the longer-term n-period horizon for both domestic and foreign interest rates: 1 XkÀ1 À Á it;n ¼ an þ Et itþjm;m ð6Þ k j¼0 XkÀ1 à à 1 à it;n ¼ an þ Et itþjm;m ð7Þ k j¼0 where k ¼ n/m.
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